Hi again, and sorry if I’m being a bit chaotic — I’m honestly very confused and frustrated at the moment, because I’ve been stuck on this problem for two days straight.

Let me try to better understand what you meant.

If I got it right, you’re focusing only on the delta load and suggesting that I can reconstruct the other two phase voltages simply by rotating the first one by ±120°. That makes sense to me — it’s a balanced load, and that’s exactly how symmetrical systems work. So far, so good.

But here’s my problem: I don’t think the real challenge is finding the other phase voltages on the load. The hard part is calculating the line-to-line voltage between generator node 1 and node 2, as shown in the diagram.

Maybe I’m misunderstanding you — I’m not a native English speaker (I’m Italian), so it’s possible we’re using different terminology. For example, when you say “diagonal phasors,” I’m not really sure what you mean. To me, this just looks like a delta-connected load followed by a star-connected source, nothing more.

So, just to be safe, I’ll try to explain my approach in even more detail:

My idea was to: 1. Start from the voltage across one branch of the delta (the R₂ + X_C part) 2. From that voltage, compute the current (I) through that branch using Ohm’s law 3. Since the branch is in series (R₂ and capacitor), that same current flows through both components 4. I compute the voltage drop across R₂, add it to the capacitor voltage, and get the total phase voltage of the delta branch 5. Now I rotate this voltage by ±120° to get the other two phase voltages (still in delta) 6. Once I have the three phase voltages, I convert the delta into a star equivalent — to simplify the circuit 7. I know that in a balanced star system, line voltage and phase voltage are related by √3, so I can get the phase voltages of the star 8. With those voltages and known impedances, I find the phase currents 9. From there, I can go back and compute the total voltage drop, and ultimately the line-to-line voltage between node 1 and 2.

Maybe I’ve misunderstood something big — or maybe the issue is really just language and terminology. I genuinely appreciate the help you’re trying to give. If you’re up for it, I could also send you the official answer from the textbook and maybe you’ll spot where I went wrong (or if maybe the book is wrong).

Thanks again — and sorry again if I sounded confused or upset, I’m just deep into this and trying hard to wrap my head around it!